Systematic derivation of hybrid coarse-grained models.

Area of Science:

• Computational physics and chemistry
• Multiscale modeling
• Materials science

Background:

• Molecular dynamics simulations are computationally expensive for large systems.
• Coarse-grained models offer a computationally feasible alternative but often lack predictive accuracy.
• The Mori-Zwanzig projection provides a theoretical framework for deriving coarse-grained models.

Purpose of the Study:

• To derive and investigate a hybrid multiscale system using the Mori-Zwanzig projection.
• To explore the coexistence of fully resolved and coarse-grained degrees of freedom.
• To analyze the impact of fine-to-coarse mapping and effective potentials.

Main Methods:

• Theoretical derivation of a generalized hybrid multiscale system.
• Numerical simulations using a parallel Julia code on a 1D nonlinear periodic system.
• Investigation of Mori-Zwanzig-derived fluctuating and dissipative terms.

Main Results:

• Demonstrated the successful coexistence of atomic and coarse-grained levels.
• Highlighted the necessity of non-constant fluctuating and dissipative terms in macroscopic models.
• Validated the Mori-Zwanzig approach for accurate reproduction of fine-grained results.

Conclusions:

• The Mori-Zwanzig approach provides a systematic way to derive predictive coarse-grained models.
• Hybrid multiscale systems incorporating Mori-Zwanzig terms accurately capture complex dynamics.
• This work advances the theoretical and practical application of coarse-grained simulations.